Linear stability analysis of the Poiseuille flow of a stratified non-Newtonian suspension: Application to microcirculation

We investigate the linear stability of a unidirectional flow of a suspension (blood) modeling the latter as a inhomogeneous non-Newtonian fluid in which viscosity depends on both the red blood cell concentration (RBCs) and the shear rate. We consider small vessels like arteries terminal branches, arterioles or venules, where the RBCs do not distribute uniformly on the cross section. The stability analysis is performed applying the classical normal-mode linear analysis. The results obtained indicate that the flow is unconditionally unstable unless the inhomogeneity of the RBCs distribution is neglected.